Aircraft: SMALL AIRCRAFT; LOW WING; 1 ENG; FIXED GEAR
Phase of flight: Initial Climb
Anomaly: ATC Issue All Types; Conflict Airborne Conflict; Deviation / Discrepancy - Procedural Published Material / Policy

LAF is not a combined Tower and TRACON as this system displays. LAF is a non-approach Tower without a radar display. Additionally; the overlaying approach control Grissom Approach (GUS) is not managed by the FAA; it is managed by the DOD. GUS approach advised LAF flight data of an IFR inbound Aircraft Y to the airport; and coordinated the visual approach from the northwest. At (XX:XX) UTC GUS Approach advised LAF flight data the arrival was approximately 22 miles northwest of the airport. At (XX:+04) LAF flight data coordinated an IFR release of Aircraft X and GUS approach released the departure and coordinated runway heading and 3;000 FT in accordance with the LOA (the release is void after 5 minutes per the LOA). At approximately (XX:+06:30) LAF Local Control requested the LAF Flight Data Controller to contact GUS Approach and verify the departure aircraft was released reference the arriving IFR aircraft. At approximately (XX:+06:42) LAF flight data contacted GUS Approach as requested and GUS Approach responded with an affirmative; and advised: 'We're going to take that guy a little bit east to get that guy out'. At approximately (XX:+07:05) GUS Approach advised LAF Flight Data that Aircraft Y was 10 miles northwest and had the field in sight. At approximately (XX:+07:05) LAF Local Control cleared Aircraft X for takeoff and instructed the aircraft to fly runway heading and maintain 3;000 as directed by GUS Approach. At approximately (XX:+07:26) Aircraft Y contacted LAF Local Control and advised they were 7-8 miles northwest on a visual approach at 3;000 FT; LAF Local Control instructed the IFR inbound to report 3 miles northwest for right downwind Runway 28. At approximately (XX:+08:31) LAF Local Control instructed Aircraft X to contact GUS Approach. At (XX:+08:54); GUS Approach contacted LAF Flight Data and stated 'Just verify that Aircraft Y will be a right downwind'; and LAF Flight Data responded 'Roger'. At approximately (XX:+13:) Aircraft Y landed Runway 28 and LAF Flight Data advised GUS Approach of the arrival time. LAF is a non-radar; non-approach Control Tower; without a radar display. Without vertical; visual; on non-radar separation; LAF Tower has no way of ensuring separation of arrival and departure IFR aircraft. Normally; GUS Approach will retain control of an IFR arrival on a visual approach until the departure is radar identified and then transfer control of the arrival to the Tower. Sometimes; GUS Approach will request LAF Tower to find the arrival aircraft visually and then request the Tower to provide visual separation; and once coordinated; switch the arrival to the Tower. However; neither occurred in this situation. From the Tower's point of view; when the arrival was switched to the Tower; there was no type of separation being provided. Perhaps the Radar Approach Control was providing some sort of radar separation. However; at the time the arrival aircraft contacted the Tower; the departure was still on the runway; and it seems impossible that radar separation between the two aircraft could have been provided. Perhaps the Radar Controller believed they had 3 or more miles laterally from the runway; but by switching the aircraft to the Tower; had no way of ensuring the arrival would remain at least 3 miles north; especially since the arrival was on a visual approach; and no restrictions were coordinated with the Tower. GUS Approach was contacted about the incident and they simply replied they had radar 'All day long' between the aircraft. The LOA states the Tower is delegated the authority to provide initial separation between departing and arriving aircraft in the Delta Surface Area. It is unclear in this situation who was responsible for separation; and if separation was ensured. A MOR was filed for loss of non-radar separation.In the past; DOD GUS Approach will not share radar or voice data during an investigation (when requested by QC following up on the MOR). The incident gets closed without a determination. Perhaps the LOA could be re-written to require GUS to share radar and voice data with the FAA when requested. There is often confusion about which facility (Tower or Approach) is going to provide separation. For example; is the Approach going to hang on to the arrival until they get control of the departure? Or does the Approach think the Tower will separate somehow and immediately switch an arrival to the Tower right after giving a departure release? The LOA could be re-written to clarify. There is too much confusion as to what kind of separation (e.g. non-radar or radar) and also who is going to provide the separation after a departure release is coordinated. The LOA could be re-written to require GUS Approach to advise the Tower when they are providing radar separation; and therefore not expecting the Tower to use some non-radar initial separation rule. If GUS is going to use radar to separate; they should tell the Tower. [Narrative #2 contained no additional information.] Reporters questioned facility LOA about who is responsible for initial separation; the Control Tower or the overlying Approach Control.